It was shown in [1] that waves in a two-layer system with free-surface boundary conditions (or in a three-layer system) can be modelled by a system of two coupled long wave equations. The study of the resonance between a solitary wave of one of the two equations and a copropagating periodic wave of the other equation is carried out numerically. The resulting wave is a generalized solitary wave....

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solitary wave solution, we obtain some special folded localized...

In this paper, we study a class of nonlinear Schrödinger equations (NLS) which admit families of small solitary wave solutions. We consider solutions which are small in the energy space H, and decompose them into solitary wave and dispersive wave components. The goal is to establish the asymptotic stability of the solitary wave and the asymptotic completeness of the dispersive wave. That is, we...

We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We construct solutions of the equations with a non-vanishing external potential corresponding to initial conditions ...

The aim of the paper is to show that splitting of a waveguide leads to fission of bulk solitons in solids. We study the dynamics of a longitudinal bulk solitary wave in a delaminated, symmetric layered elastic bar. First, we consider a two-layered bar and assume that there is a perfect interface when x<0 and complete debonding (splitting) when x>0 , where the axis Ox is directed along the bar. ...

where 3 depends’on the cross section area of the topography [see Miles’ Eqs. (5.2) and (5.3)‘]. A year later, VandenBroeck published his discovery of two smooth solitary wave solutions for the same physical model but from the perspective of direct numerical integration of Laplace equation with a free boundary and with nonlinear boundary conditions.2 One of his solitary waves is higher than the ...

In this paper, we use two different integral techniques, the first integral and the direct integral method, to study the variable coefficient nonlinear Schrödinger (NLS) equation arising in arterial mechanics. The application of the first integral method yielded periodic and solitary wave solutions. Using the direct integration lead to solitary wave solution and Jacobi elliptic function solutions.

variational iteration method using he's polynomials can be used to construct solitary solution and  compacton-like solution for nonlinear dispersive equatioons. the chosen initial solution can be determined in compacton-like form or in solitary form with some compacton-like or solitary forms with some unknown parameters, which can be determined in the solution procedure. the compacton-like solu...

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).

This paper discusses the existence and stability of solitary-wave solutions of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves pseudo-differential operators for the linear part. One of such equations can be derived from water-wave problems as second-order approximate equations from fully nonlinear governing equations. Under some conditions on the symbols of pseudo-dif...